The Save in the freehand toolbar is just to commit the annot to the PDF, but does not actually save the modified PDF anywhere. If you closed the PDF without saving, then the annotation would not appear the next time it was opened.
As for the slight movement, this is due to differences in the algorithms (iOS versus PDFNet) used to draw paths between control points. We are working on a changes to eliminate this difference, but it will be in a future (not yet scheduled release).